Problem: A circle has a circumference of $4\pi$. It has an arc of length $3\pi$. What is the central angle of the arc, in radians? ${4\pi}$ ${\dfrac{3}{2}\pi}$ $\color{#DF0030}{3\pi}$
The ratio between the arc's central angle $\theta$ and $2 \pi$ radians is equal to the the ratio between the arc length $s$ and the circle's circumference $c$ $\dfrac{\theta}{2 \pi} = \dfrac{s}{c}$ $\dfrac{\theta}{2 \pi} = 3\pi \div 4\pi$ $\dfrac{\theta}{2 \pi} = \dfrac{3}{4}$ $\theta = \dfrac{3}{4} \times 2 \pi$ $\theta = \dfrac{3}{2}\pi$ radians